Find the ratio of the outer shaded area to the inner area for a six
pointed star and an eight pointed star.

Triangle in a Triangle

Stage: 4 Challenge Level:

This is not the typical format for a problem, but the opportunity
for geometric reasoning is so rich that to make the problem
accessible at this level we have bridged some of the harder parts
of the investigation, for example using vectors to establish the
partition ratio on the interior lines, and then just given these
results as information.

The detail is included in the Hints section for those who are ready
for it.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.